Perfect Bayesian Equilibrium | |
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Solution concept in game theory | |
Relationship | |
Subset of | Bayesian Nash equilibrium |
Significance | |
Proposed by | Cho and Kreps[citation needed] |
Used for | Dynamic Bayesian games |
Example | signaling game |
In game theory, a Perfect Bayesian Equilibrium (PBE) is a solution with Bayesian probability to a turn-based game with incomplete information. More specifically, it is an equilibrium concept that uses Bayesian updating to describe player behavior in dynamic games with incomplete information. Perfect Bayesian equilibria are used to solve the outcome of games where players take turns but are unsure of the "type" of their opponent, which occurs when players don't know their opponent's preference between individual moves. A classic example of a dynamic game with types is a war game where the player is unsure whether their opponent is a risk-taking "hawk" type or a pacifistic "dove" type. Perfect Bayesian Equilibria are a refinement of Bayesian Nash equilibrium (BNE), which is a solution concept with Bayesian probability for non-turn-based games.
Any perfect Bayesian equilibrium has two components -- strategies and beliefs:
The strategies and beliefs also must satisfy the following conditions:
A perfect Bayesian equilibrium is always a Nash equilibrium.